When their old type of meter gets out of control, thousands of people are at risk of losing hot water or heating.
Energy said it would be "very, very difficult" to replace all radio tele-radio system (RTS) instruments with smart meters before the old technology is closed on June 30.
Campaigners estimate that more than 300,000 homes may lose their heating or keep sticking — called "emergency consumer welfare issues" in energy regulator OFGEM.
The government said the industry must "work eagerly to continue to increase the pace of alternatives".
Since the 1980s, RTS instruments have used long-wave RF to switch between peak and off peak.
The technology is outdated and energy companies will change customers' instrumentation by June 30.
At the end of March, 430,000 households still used RTS meter for heating and hot water.
It says that more than 1,000 RTS meters are now replaced every day.
However, based on 430,000 figures, this daily rate needs to be more like 5,000 to have the opportunity to reach everyone.
Ned Hammond, Deputy Director of Accounts at Energy UK, told BBC Radio 4 you and your replacement rate was rising, but added: "Obviously, we need to increase significantly from there to replace all the instruments by the end of June."
When asked if it is impossible to change an RTS meter by June 30, he said: "I don't want to say it's impossible - but it's obviously hard to get to that."
Simon Francis of the campaign group’s Final Fuel Poverty Alliance said that data from Energy UK suggests that more than 300,000 households may not work from July 1.
“With the pressure on alternative programs growing and the limited availability of engineers, especially in rural areas, the real risk of long-term damage, especially for vulnerable families,” he added.
Ofgem said RTS meters usually control heating and hot water on separate circuits, thus controlling electricity to other homes, so things like sockets and lights are unlikely to be affected by the shutdown.
The RTS network was initially planned to be shut down in March 2024, but this was to give energy companies more time to pass through everyone’s time.
Mr Hammond added that the energy company is still in the June 30 “things stand” goal and is developing a “system management and very cautious phase” plan to protect vulnerable customers.
The challenge of changing everyone to a new system is distrust of smart meters. The BBC has previously discovered that smart meters sometimes provide inaccurate readings and, depending on where you live, will work worse or better.
Jane of Norfolk told the BBC that she doesn't want a smart meter on an RTS meter, but feels like she's forced to get one. She is currently under the Economic 7 tariff and does not want to switch.
"Say I have to have one. I really, really don't want one. I'm very happy with the way things are going on."
Diane Gray, who lives near Cockermouth, Cumbria, uses RTS to control the heating and hot water of seven tariffs in her home economy. She wanted a smart meter but was told that a person would not work in her house.
In December, her supplier wrote to her: "At present, we cannot install a new meter in your home that works with your current meter heating settings. Please bear with us. We are working to provide solutions for your meter type."
She has since received another notice that she will install smart meters in early June.
"I don't know where it's going," she told the BBC.
"It's very worrying. Because they do it in the summer, so in the winter, I always thought there had to be some solution before we can start using the heating."
If your energy supplier is unable to install smart meters in your home, OFGEM says your supplier must install a "proper instrument" without causing disruption to the service.